Let y = 3x2 Find the change in y, Δy when x = 5 and Δx = .2 Find the differential dy when x = 5 and dx = .2

Question

Let y = 3x²

Find the change in y, Δy when x = 5 and Δx = .2

Find the differential dy when x = 5 and dx = .2

Answer 1

Let f(x) = y = 3x², x = 5, and Δx = 0.2

Δy = f(x+Δx) - f(x) = f(5.2) - f(5) = 3(5.2)² - 3(5)² = 81.12 - 75 = 6.12

dy = f'(x)Δx = 6xΔx = 6(5)(0.2) = 6